Intrinsic topological property for precise structure differentiation

Abstract

Topology in condensed matter systems, inherited from the crystalline symmetry, has aroused great research interest in recent years, yet most studies are focused on the theoretical conceptual perspective and experimental verification. Herein, we present a practical application direction of the topological orders, as the intrinsic properties of the crystalline symmetry, for precise structural differentiation. Based on first-principles calculations, we studied the electronic bands and topological properties of $\ensuremath{\alpha}$-nitrogen under the long contradictory structures $P{2}_{1}3$ and $Pa\overline{3}$. Their comparable band structures come from their great crystal structure similarity, together leading to the difficulty of precise structural determination from conventional techniques. However, when we look at the intrinsic topology from these two structures, a strong different topological feature is observed between them. A large chiral Fermi arc state is present in the $P{2}_{1}3$ structure, connecting the triple point at $\mathrm{\ensuremath{\Gamma}}$ and the Dirac point at $R$, whereas there is no such arc state in the $Pa\overline{3}$ structure. Indeed, this Fermi arc state in the $P{2}_{1}3$ structure corresponds to one of two arc states from the $\ifmmode\pm\else\textpm\fi{}2$ topological charge points at the $\mathrm{\ensuremath{\Gamma}}$ and $R$ points, where the triple point and Dirac point do not carry any charge in $Pa\overline{3}$ because of its centrosymmetric symmetry. This distinct topological behavior between these two structures can provide a definitive means for its final structure determination.